Electrical delay network



Oct. 22, 1929. l H. NYQulsT ET AL i 1,732,312

ELECTRICAL DELAY NETWORK Filed Sept. ll, 1926 2 Sheets-Sheet 1 y INVENToRs gazls KIJfZl/fer 015 1.a y; 1.15 250 i ATTORNEYS.

Oct. 22, 1929. H. NYQUIST l-:T AL 1,732,312

ELECTRICAL DELAY NETWORK Filed Sept. l1, 1926 2 Sheets-Sheet 2 TCZLJW' j??? l i5 INVENTORS By WZ A TToRNEYg Patented l STATESf-PMENT orifice HARRY NYeUIsugor 'NILLBUBR iiENNE'rH lvv. PFLEGEB, or 'mma'.roN, NEW JERSEY, AssreNons To AMERICAN TELrirHoNE AND :rameaux conrANY, A

GORPOBATION OF NEW YORK p ELEc'rnrcAL DELAY NETWORK Application iuea'sepimner 11,v 1192s.v serial No. 134,928.

. This invention relates vtofelectrical delay networks fand has for its object, the design of devices for producing delayV in the transmission ofwaveff-motion. More particularly it relates to the correction of thatform of distortion ina wave transmission system resultv ing from the difference in velocity of wavesof different fre uenciesand accomplishes this by the intr uction offan additional delay,

varying with frequency in such manner as to give an approximately equal delay Over-the frequency ran e of interest. l

Another object is .to design such a delay network which shall functionwith a given number of degrees of freedom -butwlth a i fewer number of elements than heretofore. Still a further object is to give a method ef design and design formulae of ready applicability to this network of reduced number of elements. The subject-matter' of this invention is a development and extension of certain arts of the disclosure in application of yquist, Serial No. 90,656, filed February 25, 1926.

ter understood from the following specification and the accompanying drawing in which Figure l represents a vtransmission line with a correcting transducer of a form elsewhere 33 described; Figs. 2 and 2a show details of the transducer of Fig. 1; Figs. 3 and 44 give forms which the network of our invention ma take;

work; Figs. -6 and 7 are .35 ing certain characteristics,'and which curves are used 1n the designfof our new network;

Figs. 8 and 9 give forms which 'certain parts of that network may take; Figs. 10, 1 1, 1 2 and 13 show modified forms of our circuit.

40 Referring more specifically to Fig. 1, there type,

Such a 'transducer maybe realized i The 'objects of this invention will be bea.

gven by Fic'. shows a composite section of lattice netplotted curves shove,v J..

is shown a transducer ofthe constant 3K?. l

i. e., the characteristic impedance is independent ,of frequency. Let this `be a transducer of no attenuation and total phase vshift and ywhose propagation constant is therefore given by P 0 1lj, Where 1/ 1 wehave n' sections of lattice type networks 'of the kind shown enerically inl Fig. 2`and1 more, particularly inFig. 2, in which all elements are free from resistance.. For such a transducer it can be shown that the characteristic impedance kis K= JZ1Z2/4 `and if K is to be maintained constant this can be assured by We will show now that the circuit of Fig. 1 can be replaced by the hybridcoil arrangement of Fig. 3 or the simpler one of Fig. 4, both of these possessing the transformer' connections characteristic of the so-called 22- type repeater circuit. kIn these figures, Z, and Z4 represent the impedance of the incoming and outgoing lines. Y y p' It can be shown by use of ordinary circuital equations that the current-z2 in Fig. 4 is where rnis lthe ratio of turnsin the windin s f3 and 4. In this case let n=1/2, Now su stitutingK for Za and Zand the above valuesA 30 work of is,

ipsaeie ter there isreection with a changel of phase of 1r radians. I

" i lbut.the"valu-eior the output current :from the far termnalso'f the sections of lattice netf v land by reversing a terminal lz.

Thus? it is seen that a plurality of tandem sections vof non-dissipative lattice network,

l f each withitsfflmembers, serving as a transducer in Fig., .1', can be replaced by ahybrid reactance vZ1 and ZZ. y Referring again to Fig.. 4:, it will be ob l 'I servedthat a wave coming in from e and en- .tering the'impedance Z1, will be redectedat the end of'Z1 and traverse it a ain.. If the phase displacement correspon ing to one 'placement will be If now Z2 is such that its 1 .total phase' displacement ditfers from. this by Y the anglearthen the two reflected components will annul each yother so far as the current back tothe source is concerned but will be additive in the secondary of the transformer. Thus, the wave is propagated forward but with a delay or phase displacement determined by Z1 and Z2.

` One way in which this phase difference of an angle fr can be realized is by use of the relationship ofEquations (l) and this may be obtained in a particular case by using one half of the transducer of Fi 1 as Z1 and as Z2, the one of these being s ortscircuited at the further end and the lother being open-` circuited. In the former case, as is Ywell known, there is a reflection ofthe current wave Without change of phase and in the laty :oilfand two members liavlng non-dissipative' l lattice. This may be looked upon as due to thel fact that in Figs. 3 or 4, the waves, because of reflection, must traverse the impedances Z1 andZ2 twice, thus introducingvthe j2K tan '-icot) *l n 5 FE *l `jZKtan 2f j2K cot 5+ K-l# K -J2K cot Ki Ii')-I4Kz l- E(tan2+cot2) 1 'ifi-"V v tan 2K-j2l cot 2K cot 541712K' .E tan%t cot l. I 2K tan 5.- cot --J 2) p but Although we have spoken of thus replacsin ing 'n sections of lattice network, it will bev 20' tan E" (i @0s observed that the treatment is not limited to 'and a plurality of sections but wouldho'ld equally ,3 sm well for a single section, and in this case,

cot' "2T: 1.. C OS the impedances Z1 and Z2` would'each corref f -f spond to one of the four members of thelat- 25. n tice thus requiring only half as many ele- "2K 00S +2 S111 ments of inductance and capacity as in the required retardation or phase displacement.

An essential part of our invention consists in the economy of re uired elements `for a given delay introduce in this way and the importance of that feature may be more evident when it is recognized that n sections of such lattice networks can be replaced by a single lattice section, the members being made complex, as shown in Fig. 5, and containing the same number of elements as the n sections. By the hybrid coil arrangement, then, the given delay or .phase displacement may be obtained by the use of two of the four complex members or their equivalents and thus the number of elements reduced to onehalf.

The method which we have devised for designing the electrical networks Z1 and Z2 for any particular case is illustrated by the following: Suppose a medium heavy loaded side circuit, 222 miles long, is tobe corrected for transients over the range 80G-1800 cycles for picture transmission. The delay character-- to that of curve a over the specified frequency range, and oury problem is that of finding the constants of the impedances Z1 and Z2 of Fig.

where b isa constant depending :on the capac- 1t1es and lnductances of any one section and determines the amount of delay for that secodolosese ll ll Il @worden tion at different frequencies. This is shown in Fig. 7 where Tf., is plotted against f/.f0 for different values of b. Here T representsthe time of delay of a section of the form of Fig. 2a and fo represents the resonant frequency of the members of the section. Also f1, f2, f3 in the table denote the .resonant frequency of the members of the network in' question and means the same as fo in Fig. 7.

The delay, introduced by anyone section, can be found from the following considerations: For the lattice type network If we keep K constant by making Z1 =K Z and ly to the impedances -iH (1221-` p2) (Pza-p2) (pzmwpz) (pms-p2) from which the curves of Fig. 7 can be plotted.

Let it be desired to replace the six section network by the equivalent hybrid coil arrangement which uses only two members Z1 and Z2, as in Fig. 4.

for each section of network.

The Equation (1) ,plotted vs.- frequency, f, gives a curve proportional directly or inversewhich are desired (see curve C of Fig. 6). Whenever is zero or a multiple of 1r, the impedance is zero or infinite. These frequencies can be determined by plotting vs.j and observing at what v values off the curve of crosses 0, 1r, 2r, 31|,

etc.

There are several Ways to simulate Z1 and Z2. One method is that using Fosters Re- .actance theorem, published in Bell System 'Technical Journal, Vol. III, No. 2, p. 259,

whichA states: The driving point impedance S of a finite resistanceless network Whose resonant frequencies (i. e., S=0) areI and `whose anti-resonant frequencies (i. e., S= oo) are:

etc.

` 1)(122' LetZ be the series`resonant circuit, then tan Where H is aconstant factor o and o= @512151925 .2121.-. S p2= H may e calculated from the value of S at some particular frequency from the curve C of Fig.

(i and preferably at other than' a resonant or anti-resonant frequency.

In order to cover all possible cases, p1 may sometimes equal po and 10%1 may become 1nfinite while Hp2 is maintained finite.'

For example, if the impedance to be constructed is resonant at zero and infinity, then we will let p.,rp,=0` and p2 ,==p2= oo.

This is illustrated by the calculation of Z1 following. We do not actually use either p0 or p2., in this case but p2...14 must represent the highest resonant frequency' andthere must be a frequency 112,. p2 1. We can think of them as p2 1= and p2= o 1 for for the sake of convenience. Similarly if the desired impedance were resonant at zero and anti-resonant at infinity we Ywould have highest resonant frequency and not inlinity. Keeping the above in mind together with the fact that resonant frequencies have odd subscripts and anti-resonant frequencies have even subscripts, it is possibleto assign the proper values for p0, 01, etc., from any given impedance curve. S may be represented, as in Fig. 8, by parallel resonant circuits eachhaving a coil and condenser in series resonating at the frequencies f1, 7f3, f5, etc., or,

as in Fig. 9, by a series of anti-resonant circuits each having a coil and condenser in parallel resonating at fo, f2, f4, etc., as shown in Figs. 8 and 9.

llt should be pointed out that the impedances Z1 and Z2 of Fig. 4 mi be of the form of Fig. 8 or Fig. 9, as descri ed, and both of them may be of the same form or they may be of different forms. Also, other equivalent forms may be used, but the discussion here will, for simplicity, be conhned to those of Figs. 8 and 9. lin any case, however, the

' values ofthe inductances and capacities must be so chosen that for one of them there shall be a series of resonant frequencies, p1, p3,

` 292ml, with an anti-resonant frequency, p2,

p4 122,., between each of the resonant frequencies and that for the other, a similar condition holds With the further condition that` the anti-resonantl frequencies of the one shall be the same as the resonant frequency of the other.`

While the constants of these two circuits may be obtained from Fosters theorem, We shall now show that certain constants for either Z1 or Z2 made in the form shown above can be calculated from the formulae (5) and (6), which are much simpler:

for resonant circuits in parallel or for anti-resonant circuits in series.

ln the above T2, is the delay in seconds at ythe frequency fem; and T2z is the devlay at the frequency 72,.

These Equations (5) and (6) are funda mental in our method of `design and constitute our design formulae. However, the` boundary conditions introduce certain other relations which must be used and We will novv derive these. Looking at Fig. 8 it will be apf parent that if this network 1s tobev used for Z1, it must have, according to curve C di Fig. 6, a zero impedance at zero requenc' (i. er., C1= oo) and it must-have zero `iimpe ance at infinite frequencyfi. e.l L2, 1=0). Also,if Fig. 9 is to beused for Z1, the same impedance araaaia conditions must hold (i. e., C0= oo and L2=0) Furthermore, in Fig. 8, the impedance at inlinite frequency will be that of ca-V pacity Cznqsince llama1 has been made zero and since all other capacities have series inducytance. This impedance will be and on giving thisvalue to S in Equation (4) arlid allowing p to approach infinity, it is seen t at At first glance, it looks as though 02M 'would be zero because p2 1= oo, but H includes the factor lt will be shown below that U0 4 K- Bringing these relations together tor ready reference We have:

lTo prove Fquations`(5) and (6), let Z2 be represented by S=j2K cot ,8/2, then from y Equation (l), it follows that:

or 2 tan1 Writing the expression for S from the above ligure We` get v c=,n-l

:v f nickle) 'Sl wir l We". 'from Fig. 9, and: Y U

-:n-llmgi@ S 33:() 'LmeiPu-H-Pz) from Fig. 8.

Substituting the value of S (from Fig. 9) into the first form of Equation 8 for delay and simplifying gives to the other terms in both numerator and denominator so that they may be neglected.

Values of To, TN, and TQM from the delay curve (b), Fig. 6 may be used to compute C0, C23, LM, Cam, L22H by the above equations.

H(=L2) may be determinedfrom the expression for S at any frequency. The first two columns relate to Fig.'9 and the last two to Fig. 8. It depends on the value of K or Therefore the sizes of coils and condensers available T5241( C., (10) see (7) whether the resonant or the anti-resonant arf p h rangement is the cheaper. Slmllarly as the requency `2Tf approa'c es Values for Z2=S, taking K=600 ohms.

00 .2792X10fd. Lo oo henry 01 :.1736 X10'6fd.' L1 .5040 02 .835sx10-6fd.. L2 =.05721 03 =.01986 10Gfd. L8 :1.851 04 =-1.212 x10-61d. L4 =.02511 05 :.0153 X10-afd. L5 =1.653 06 =1.031 x10-efe. L =.02052 0, =.01260 10fd. L, =1.401 Us .83 96X10fd. L8 :.01753 0 =.01309 X10'6fd. L9 .9150 om: .3542x10-6fd. L1=.02570 0=.04195 10Lfd. Ln= .1170 012= 0 L12=.07372 any particular value gz the term containingy 2a' subscripts becomes large compared to the `Substituting the value of (from Fig. 8)

into the second expression for delay and simplifying gives:

By reasoning similar to that 'above We see that at the frequency Let us now use these equations to find the constants of Z2. Since Z2 is anti-resonant at zero and infinity we know that f0=0 and Since Z1 is proportional to the curve for S l 1 B- 2 cot or 2 ltan 7.2K

2 (11) tangthe frequencies are as follows:

im.: oo. The various frequencies, as found AS 'already pOiIlted 0l1t ,f01` Z1 from curve C of Fig. 6, are as follows:

2F: 728. f1: 538 f4= 912` f3: 830 f=1094 f 998 f 8:1312 f 7:1198 f10=1668- -1454 f12= fix-C2272 in order that the impedance be zero for the frequencies 0 and oo Now proceeding as before:

Substituting the value of into the first form of (12) and simplifying gives:

essary and are determined by the lattice net- I work which gives curve b. It is not necessary o 1 :D n 2 p2 p22 4K z+1 n- P2L1+ 1 L2z+1(P22r+1 :P202 g2 'l (13) K2( 1 @5nd p C' y 1 4 n-. -pLl =1 L2z+1(P22z+1-P2) p 2 l `At the frequency 12:0 terms not containing network and the use of the resulting curve b i L1 are negligible: as an important step in our method of design.

L In order to make more evident the proce- T0=1I (14) See (7) dure which We follow in order to design the delay or phase compensator which is dewhen PL-pzm terms not containing L2I+1 are scribed in this specification, we give below a negligible: brief'summary of the steps which may be L taken. First, a plot of the desired delay char- T2m=2 `2I+1= (5) acteristic, such as that of curvea, Fig. 6, is K Klzml 02x41 made. Then a lattice network o f a` desired Substituting the value of S into the second number (1f lectlons Whlch Wm gw; a elay expression for delay and simplifying gives: g1slctpggagl tltsccgg l =fn 1 2 2 with the method diszlosed in the Patent -1- 2 (p 1,675,460 referred to above. In this way, the T En: 1 (l) P curve b of Fig. 6 is obtained. We then find ,8,

m: fn,- 1 2 2 the phase shift, at various frequencies corre- 1 4. E P ZPL) sponding to this curve b and plot the values of l P 2z p tan g from these values thus obtaining the Whnce .t curve C of Fig. 6. The ordinates of this curve T2=-V8K =8KU2E (6) C will not only be equal. to tan but, aS

P 2x LM 2 Values for Z1 A U., @o Lo @o 01 0o fd. L1 .402 U2 :1.4L XlOBfd. L2 :.06667 henry Us :.O397OX10'8 L3 :4.012 U4 :5.142X10fd. L4 :.007148 05 :.01744X10 L5 :1.746 06 :4.592X106fd. L6 :.005537 07 :..OllQXlOe L., :1.485 Us :3.892X10-1d L8 :.004535 U9 :.012lfZ'Xl0e Le :1.209 010:2.542 X 10*fd. L10=004713 U11-5.01785 X 10 in: .510 012= .325x 10-6101. 2:0151 1 013:.05119X 10*6 L13: o f 01a: 0 Lif: 0 I

The same considerations govern the choice shown in this specification, will also be equal between series anti-resonant circuits and part Z1 d 2K F th. C h allel resonant circuits for Zl as for Z2. o an TZ; rom 1s curve t er@ The question may be' raised Whg/use is made will be located immediately certain points at of the curve b of F 1g. 6 instea. of curve a,` y since the latter relates to the line to be correct- Whlch tan 27 is equal to Zero or to mmty ed md Since th@ OImr calls for the design these corresponding to frequencies Where of the lattice network which shall have a deis, a multiple of 186. and corresponds also to lay c urve slmllar to curve a. rl`he reason for lthe frequencies where the new networkwill this 1s, that the Values for bn and fn are-.necbe resonant or anti-resonant. The delay, T,

' which will give a network ofthe desiredphase at each of these resonant and anti-resonant curve b. It will now be desirable to select the form of impedance, such as that of Fig. 8 or Fig. 9, and inspect this for the boundary conditions, and also to determine the value of the constant K, and, finally, the value of T and K is substituted in relations containing T, K, L, C and the frequency as given in the Equations 5 and 6, (first form) such substitution yielding the particular values of L and C characteristic.

What is claimed is: l. A phase delay compensator adapted to be associated wlth a transmission line andl comprising a transformer and a complex impedance, said impedance having resonant and anti-resonant frequencies, the constants of the impedance being so chosen as to give the same delay as an equivalent n section lattice network at each of the aforesaid resonant and anti-resonant frequencies.

2. A phase delay compensator adapted to be associated with a transmission line and comprising a transformer and a complex impedance, said impedance having resonant and anti-resonant frequencies, these frequencies being those at which the phase shift of an equivalent n section lattice network is a multiple of 180, and the values of the inductances and capacities in said impedance being determined by the .impedance of the transmission line and the delay to be obtained at the resonant and anti-resonant frequencies.

3. A phase compensator adapted to be associated with a transmission line and being the equivalent of an n section lattice network and comprising a hybrid coil and a complex impedance, said impedance having resonant and anti-resonant frequencies, the constants of the impedance being determined by the vdelay in said equivalent lattice network at each resonant and anti-resonant frequency of the complex impedance, and by the impedance of the transmission line.

4. A phase compensator adapted to be associated with a transmission line and being the equivalent of an n section lattice network` and comprising a hybrid coil and a complex impedance, said impedance consisting of fn parallel branches of series inductance and capacity and having .resonant and anti-resonant requencies, the values of the inductances and capacities being determined by the delay of the equivalent lattice network at each resonant and anti-resonant frequency and the impedance of the transmission line to yield the same delay as in the lattice network.

5. A phase compensator adapted to be associated with a transmission line and being the equivalent of an n section lattice network and comprising aghybrid coil and a complex impedance, said impedance comprising n sec- 'tions in series of shunt inductance and capacity and having resonant and anti-resonant frequencies, the values of the inductances and capacities being determined by the delay of the equivalent lattice network at each resonantand'anti-resonant frequency and the impedance of the transmission line toyield the same delay as in the lattice network.

6.- A phase compensator adapted to be associated with a transmission line and' comprising a hybrid coil and two complex impedances and being the equivalent of an n section lattice delay network, one impedance having resonant and anti-resonant frequencies, the other having equal anti-resonant and resonant frequencies, the constants of the inductances and capacities being determined by the delay in the equivalent lattice network at each resonant and anti-resonant frequency.

7. A phase delay compensator adapted to be associated with a transmission line and comprising a transformer and a complex imedance, the delay characteristic being made equal to that of a previously chosen n section lattice network, said impedance having res-.

onant and anti-resonant frequencies, the elements of the impedance having such values as to yield the same delay at the aforesaid 'late an n section lattice delay network, the

combination of a hybrid coil with output terminals unaffected directly by current introduced at the input terminals, and a network to receive currentfrom the input terminals and refiect it back, the system being adapted to make the reflected current waves effective on the outputterminals, the elements of the network being so chosen that the over-all delay characteristic shall be that of the n section lattice network.

9. In an electrical wave transmission system, the combination of a transmission line with delay characteristics and a delay compensator, said compensator .comprising a hybrid coil with output terminals unaffected directly by current introduced at the input terminals, and a network to receive current from the input terminals and refiect it back, the systembeing adapted to make the refiected current waves effective on the output terminals, the elements of the network being so chosen that the over-al1 characteristic shall be the inverse of that of the ytransmission line.

10. In an electrical delay network to simulate-an n section lattice elay network, the combination of a hybrid coil with output terminals unaffected directly by current introduced at the input terminals, and a network to receive current from the input terminals -tive on the output terminals, the network having half as many elements as in the lattice network and vhaving resonant and antiresonant frequencies, the elements of the network having such values as to yield the same delay at the aforesaid resonant and anti-resonant frequencies as in the lattice network.

11. A delay network comprising a hybrid coil with putput terminals unaffected directly by current introduced at the input terminals, and two complex impedances to receive and divide current from the input terminals and reflect it back, the one impedance reflecting with change of phaseand the other Without change of phase to make the reflected waves effective on the output terminals.

12. A delay network comprising a hybrid coil with output terminals unaffected directly by current introduced at the input terminals, and two complex impedances to receive and divide current from the input terminals and reflect it back, the one impedance being resonant and anti-resonant at certain frequencies, and the other impedance being anti-res-V onant and resonant at the same frequencies.

13.` A delay network to simulate an n section lattice delay network and comprising a hybrid coil with output terminals unaffected by current introduced at the input terminals and two complex impedances to receive and 'divide current from the input terminals and reflect it back, the one impedance reflecting with a change of phase and the other without change of phase to make the reflected waves effective in the output terminals, the elements of the impedances being half as great in number as in the lattice network ard having values to yield the same delay as in the lattice network.

14. A delay network comprising a hybrid coil with output terminals unaffected directly by current introduced at the input terminals, and two complex impedances to receive and divide current from the input termlnals and reflect it back, the two impedances reflecting with a difference in phase of 180 to make the reflected waves effective on the output terminals.

15. In combination, a transmission line and a phase delay compensator of a delay characteristic equivalent to that of an n section lattice network, said compensator comprising a transformer and a complex impedance, the number of elements of the complex impecl` ance being half that of the lattice network, and its constants having values determined by plotting the desired delay characteristic, finding the lattice network of n sections whose delay characteristic approximates this, locating the resonant and anti-'resonant frequencies for said complex impedance, finding the delay at each of said resonant and anti-resonant frequencies, and obtaining the constants of the complex impedance from this delay and from the characteristic impedance of the line.

16. A phase compensator of a delay charac teristic equivalent to a delay network of n lattice sections and comprising a transformer and a complex impedance, the constants of the complex impedance havin'g values determined by plotting the desired delay characteristic, finding the eqivalent lattice network of n sections, finding the angular shift as a function yof frequency for this lattice network, locating the frequencies where this shift is a multiple of 180, finding the delay at each of these frequencies, and obtaining the inductances and capacities of the impedance from this delay and the characteristic impedance of the lattice network.

In testimony whereof, we have signed our names to this specification this 10th day of September, 1926.

HARRY NYQUIST.

KENNETH W. PFLEGER. 

